Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to approximate f(1.02, -1.97) without a calculator.

Q: MTH 32 (16) Show that f is one-to-onc. Find (f-¹)'(a). Calculate f-¹. Find the domain and range for…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: -22 - x2, find f(x), f(x), f(x), and f(4)(x). " (x) 70 = aph f, f', f", and f" on a common screen. y…

A: Given query is to find indicated derivatives.

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Q: Find all points (x,y) on the graph of f(x) = 2x3 + 1 with tangent lines perpendicular to the line y=…

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Q: Find the derivative of the function at the given point in the direction of A. f(xy) = 5x2 + 4y, (-…

A: We have to find the derivative of the function at the given point in the direction of A.…

Q: 1) Estimate T'(3). Show the work that leads to your answer. Include units of measure. ) Write an…

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Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: the velocity of a projectile is found using the function v(t) = t^2 + 16t and is measured in feet…

A: Using application of differential equations.

Q: Use the First Derivative Test to find the relative extrema of ƒ(x)=· sin x on (0,27).

A: The given function is- fx=x2-sinx  Differentiating f(x) w.r.t x- f'x=12-cosx Put f'x=0,…

Q: One method to obtain an approximate solution is to plot the function and determine where it crosses…

A: True  is correct ans

Q: Consider the following function: Step 1 of 4: Determine ƒ'(x) and ƒ"(x). f(x) = (x − 1)(x+8)² Answer…

A: Step 1:To determine f′(x) and f′′(x) for the given function f(x)=(x−1)(x+8)2, we can use the product…

Q: Find the derivative of f (y) = 8 tan (y) V √y 8 8 √Y y4

A: The given function is: fy=8tany-y8-8y4y As we know that; The Sum/Difference rule: f±g'=f'±g' The…

Q: The following quadratic function is given: f(t) = 5t²-7t + 25. i) ii) Use first principle to find…

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Q: f (1, 2) = 3 and the derivative of the function f at the point (1, 2) in the direction of i + j is…

A: The given problem is to find the approximated value of f(1.1,2.1) from the given information of…

Q: Where is the function y =4x/x-3 concave downward? Show mathematical work to clearly answer this…

A: For a given function y=f(x) the curve is concave downward in an interval I when the second…

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A: We have to find

Q: Consider the function -3 f(x)=√1+z² (a) Find the linearization of the function f near z = 0. In…

A: Consider the function near (a) The linearization of a function is given by In our case, Evaluating…

Q: Estimate f(5.07) for f as in the figure. y y = f(x) (10, 4) Tangent line (4, 2) (Give your answer to…

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Q: Find an equation of the tangent line to y = f(x) at x = -2. (Using the definition) f(x)=x² + x² + x…

A: we have, Differentiating w.r.t x, we getDifferentiating again w.r.t x, we getFurther,    .     .…